At 09:41 -0400 14/7/10, jimialeggio wrote: >... I guess it turns out the the calc uses vectors rather than the >high school trig we are usually use. > >Geeks who understand vectors seem to do all kinds of cool and >bizarre things with them... Sure, but vectors (as such) don't really come into this; it's simply the same old basic trig applied to a very elementary mechanical law. Most of us were taught both before we ever heard of a vector. The distance of the string/bridge contact above the horizontal would be calculated by multiplying the speaking length by the SINE of the angle, so the longer the string, the greater that distance is for a given angle, but by elementary mechanics the force (the tension) will be shared in the same proportion between the x axis and the y axis, so the length of the string is immaterial; only the angle and the tension are needed for the calculation. In this case we are dividing the force between the y axis and a line sloping up from the x axis, so we use the SINE rather than the TANGENT. JD
This PTG archive page provided courtesy of Moy Piano Service, LLC